The Moore Bound for Irregular Graphs

 What is the largest number of edges in a graph of order n and girth g? For d-regular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular graphs as well, yielding an affirmative answer to an old open problem ([4] p. 163, problem 10). Received: June 27, 2000 Final version received: July 3, 2001     

Nuclear equation of state and compression modes

The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K _nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K _nm and the experimental and theoretical methods used to determine the value of K _nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR.     

Properties of isolated DNA bases, base pairs and nucleosides examined by laser spectroscopy

The vibronic spectra of laser desorbed and jet cooled guanine (G) adenine (A), and cytosine (C) consist of bands from four, two and two major tautomers respectively, as revealed by UV-UV and IR-UV double resonance spectroscopy. The vibronic spectrum of adenine around 277 nm consists of weak nπ^* and strong ππ^* transitions, based on IR-UV and deuteration experiments. Precise ionization potentials of G and A were determined with 2-color, 2-photon ionization. We also measured vibronic and IR spectra of several base pairs. GC exhibits a HNH ^... OH/NH ^... N/C=O ^... HNH bonding similar to the Watson-Crick GC base pair but with C as enol tautomer. One GG isomer exhibits non-symmetric hydrogen bonding with HNH ^... N/NH ^... N/C=O ^... HNH interactions. A second observed GG isomer has a symmetrical hydrogen bond arrangement with C=O ^... NH/NH ^... O=C bonding. Two CC isomers were observed with symmetrical C=O ^... NH/NH ^... O=C bonding and nonsymmetrical C=O ^... HNH/NH ^... N interaction, respectively. Guanosine (Gs), 2-DeoxyGs und 3-DeoxyGs each exhibit only one isomer in the investigated wavelength range around 290 nm with a strong intramolecular sugar(5-OH) ^... enolguanine(3-N) hydrogen bond. Received 16 June 2002 / Received in final form 15 July 2002 Published online 13 September 2002     

CONFLICT AND COOPERATION IN UTILIZING A COMMON PROPERTY RESOURCE

Noncooperative games are used to demonstrate that, while free riding is always an option, the “tragedy of the commons” is not inevitable. When the decision to cooperate or free ride is considered in a dynamic setting, there is no intermediate case where some cooperate and others free ride. The game is only stabilized in either full cooperation or full defection. The important factor in obtaining a cooperative outcome is the critical number of players that decide to cooperate. The concept of commitment is used to demonstrate the necessary and sufficient conditions for full cooperation. Although the analysis is based on a shared water resource, it can be extended to other natural resources with common costs and private benefits, especially in the cases where there are no international authorities or treaties that internalize the externalities involved in privatizing the resource.     

A new class of long-tailed pausing time densities for the CTRW

We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln¹⁺(t/T)]^–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r ²(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form.     

Properties of noninteger moments in a first passage time problem

We calculate the moments t ^q , whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t _q ~L (q) asL, then we show that there is a phase transition atq=q _c such that whenq<q _c ,(g)=0, and forq>q _c , (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.     

Synthesis and characteristics of microspheres of polystyrene derivatives

Two sytrene derivatives formylstyrene and styrene sulfonylcholoride, were synthesized. Polymeric microspheres in diameters ranging from 0.1 to 2 μm were synthesized by polymerization of chlormoethylstyrene, formylstyrene, and styrene sulfonylcholoride in organic solvents, in the presence of appropriate surfactants. The kinetics of microsphere formation were studied. The molecular weight distribution of the products was determined by gel permeation chromatography. Conditions for binding various amino ligands to the microspheres were also established.     

Effect of solvents on the electrochemistry of olefins and aromatic molecules

Cyclic voltammetry and electrolysis studies were carried out in dimethyl sulfoxide, diglyme and liquid ammonia. The depolarizers were diethyl fumarate, ethyl cinnamate, stilbene and anthracene. The reduction reactions were carried out in the presence of organic halides, phenol, acids and water. The rates of the reactions were measured. The main solvent effect was noticed with water which reacts 100 times faster in diglyme than in liquid ammonia or DMSO. The results of electrolytic experiments with two reactants simultaneously were compared with those predicted from the kinetic data.     

High-throughput screening of enzyme libraries: thiolactonases evolved by fluorescence-activated sorting of single cells in emulsion compartments

Single bacterial cells, each expressing a different library variant, were compartmentalized in aqueous droplets of water-in-oil (w/o) emulsions, thus maintaining a linkage between a plasmid-borne gene, the encoded enzyme variant, and the fluorescent product this enzyme may generate. Conversion into a double, water-in-oil-in-water (w/o/w) emulsion enabled the sorting of these compartments by FACS, as well as the isolation of living bacteria cells and their enzyme-coding genes. We demonstrate the directed evolution of new enzyme variants by screening >10(7) serum paraoxonase (PON1) mutants, to yield 100-fold improvements in thiolactonase activity. In vitro compartmentalization (IVC) of single cells, each carrying >10(4) enzyme molecules, in a volume of <10 femtoliter (fl), enabled detection and selection despite the fast, spontaneous hydrolysis of the substrate, the very low initial thiolactonase activity of PON1, and the use of difusable fluorescent products.     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.